Try It

Practice Problem #1

Are these lines perpendicular?

First line as points at (0, 1) and (1, -2). Second line as points at (-1, -1) and (1, 0)

Answer: no

Practice Problem #2

Are these lines perpendicular?

First line with points at (-1, 1) and (0, -3). Second line with points at (-4, 0) and (0, 1)

Answer: yes

Practice Problem #3

Are these lines perpendicular?

y = 3x + 4 and y = 3x - 2

Answer: no; One line has a slope of 3. The other line has a slope of 3 as well. The slopes are not negative reciprocals, so these lines are not perpendicular. In fact, they are parallel.

Practice Problem #4

Are these lines perpendicular?

y = -2x + 1 and y equals one-half x minus 5

Answer: Yes; One line has a slope of -2. The other line has a slope of 1/2. The slopes are negative reciprocals, so these lines are not perpendicular.

Practice Problem #5

Are these lines perpendicular?

y - 3x = 5 and y = negative 1 third x + 2

Answer: yes; Before you can answer this, make sure you get the first equation into slope intercept form by moving the x-term to the left side. y = 3x + 5. One line has a slope of 3. The other line has a slope of - 1/3. The slopes are negative reciprocals, so these lines are perpendicular.

Practice Problem #6

Find the equations of a line in slope intercept form that is perpendicular to the line y = 2x - 3 that goes through the point (4, 1).

What is the slope of the given line?

Answer: 2

Ok, now that we know the slope of the given line, what is the slope of a line perpendicular to it.

Answer: - 1/2

Now that we have the slope as - 1/2, we can substitute this value and the points into point slope form to find the equation in slope intercept form.

y - y1 = m(x - x1)

y - 1 = -1/2 (x-4)

Distribute the -1/2 across the terms in the parentheses.

y-1 -(1/2)x + 2

Isolate the y-term.

y - 1 +2 = - (1/2)x + 2 + 1

Combine like terms to simplify.

y = -(1/2)x = blank

Answer: 3